Mechele Neal Statistics Assignment 4dProblems 14.15, 14.28, 14.30, 14.35, 14.44 and 14.5014.15 What is the SStotal? The sum of squares total, SStotal, represents the worst-case scenario, the total error we would have in our predictions if there was no regression equation and we had to predict the mean for everybody.14.28 Write the equation for the line of prediction using the following output from a multiple regression analysis:ModelUnstandardized CoefficientsStandardizedCoefficientst3.3334.313-1.704Sig0.0010.0000.093BStd ErrorBeta1 (Constant) Variable 1 Variable 23.977.414-0.0191.1930.0960.Mechele Neal Statistics Assignment 4d

Problems 14.15, 14.28, 14.30, 14.35, 14.44 and 14.50

14.15 What is the SStotal? The sum of squares total, SStotal, represents the worst-case scenario, the total error we would have in our predictions if there was no regression equation and we had to predict the mean for everybody.

 

14.28 Write the equation for the line of prediction using the following output from a multiple regression analysis:

 

 

 

Model Unstandardized 

Coefficients Standardized

Coefficients

 

t

 

3.333

4.313

-1.704

 

Sig

 

0.001

0.000

0.093   

  B Std Error Beta   

 

1 (Constant)

  Variable 1

  Variable 2

3.977

.414

-0.019

1.193

0.096

0.011

 

0.458

-.181  

Dependant variable : Outcome (Y)

 

 

14.30 Use the equation for the line you created in Exercise 1 4.28 to make predictions for each of the following:

a. Variable 1  = 6, variable 2 = 60

b. Variable 1 = 9, variable 2 = 54.3

c. Variable 1 = 1 3, variable 2 = 44.8

 

 

 

 

 

1 4.35 Running a football stadium for an NFL team involves innumerable predictions. For example, when stocking up on food and beverages for sale at the game, it helps to have an idea of how much will be sold. In the football stadiums in colder climates, stadium managers use expected outdoor temperature to predict sales of hot chocolate.

a. What is the independent variable in this example?  Outdoor temperature

b. What is the dependent variable? How many hot chocolates expected to be sold

c. As the value of the independent variable increases, what can we predict would happen to the value of

the dependent variable? Increase in outdoor temperature will decrease hot chocolates sold.

d. What other variables might predict this dependent variable? Name at least three. How many people came to the game, how many people like hot chocolate, how much money people have to spend at the game. 

 

1 4.44 Exercises 1 4.39, 1 4.41 , and 14.43 used the example from How It Works 1 3.2 on whether age can predict how much people study. Here are the data once again.

 

Number of Hours 

Student Age Studied (per week)

1 1 9 5

2 20 20

3 20 8

4 21 1 2

5 21 1 8

6 23 25

7 22 1 5

8 20 1 0

9 1 9 1 4

1 0 25 1 5

Calculate the proportionate reduction in error the long way.

Explain what the proportionate reduction in error that you calculated in part (a) tells us. Be specific about what it tells us about predicting using the regression equation versus predicting using the mean.

Demonstrate how the proportionate reduction in error could be calculated using the short way. Why does this make sense? That is, why does the correlation coefficient give us a sense of how useful the regression equation will be?

 

 

1 4.50 We analyzed data from a larger data set that one of the authors used for previous research (Nolan, Flynn, & Garber, 2003) . In the current analyses, we used regression to look at factors that predict anxiety over three-year period. Here is the output for the regression analysis examining whether depression at year 1 predicted anxiety at year 3. 

 

 

Coefficients (a)

 

 

Unstandardized 

Coefficients Standardized

Coefficients

 

t

 

43.665

3.333

 

 

Sig

 

0.000

0.001

  

  B Std Error Beta   

 

 (Constant)

Depression Year 1

 

24.698

.161

 

.566

.048

 

0.235

 

    a dependent variable : Anxiety Year 3

 

a. From this software output, write the regression equation.

b. As depression at year 1 increases by 1 point, what happens to the predicted anxiety level for year 3?

Be specific.

c. If someone has a depression score of 10 at year 1, what would we predict for her anxiety score at

year 3?

d. If someone has a depression score of 2 at year 1, what would we predict for his anxiety score at year 3?